{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## 项目 : 预测波士顿房价\n",
    "\n",
    "\n",
    "欢迎来到 DSVC 《机器学习》研讨班第二周的项目！在此文件中，有些示例代码已经提供给你，但你还需要实现更多的功能来让项目成功运行。除非有明确要求，你无须修改任何已给出的代码。以**编程练习**开始的标题表示接下来的内容中有需要你必须实现的功能。每一部分都会有详细的指导，需要实现的部分也会在注释中以**TODO**标出。请仔细阅读所有的提示！\n",
    "\n",
    "除了实现代码外，你还**必须**回答一些与项目和实现有关的问题。每一个需要你回答的问题都会以**'问题 X'**为标题。请仔细阅读每个问题，并且在问题后的**'回答'**文字框中写出完整的答案。你的项目将会根据你对问题的回答和撰写代码所实现的功能来进行评分。\n",
    "\n",
    ">**提示：**Code 和 Markdown 区域可通过 **Shift + Enter** 快捷键运行。此外，Markdown可以通过双击进入编辑模式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第一步. 导入数据\n",
    "在这个项目中，你将利用马萨诸塞州波士顿郊区的房屋信息数据训练和测试一个模型，并对模型的性能和预测能力进行测试。通过该数据训练后的好的模型可以被用来对房屋做特定预测---尤其是对房屋的价值。对于房地产经纪等人的日常工作来说，这样的预测模型被证明非常有价值。\n",
    "\n",
    "此项目的数据集来自[UCI机器学习知识库(数据集已下线)](https://archive.ics.uci.edu/ml/datasets.html)。波士顿房屋这些数据于1978年开始统计，共506个数据点，涵盖了麻省波士顿不同郊区房屋14种特征的信息。本项目对原始数据集做了以下处理：\n",
    "- 有16个`'MEDV'` 值为50.0的数据点被移除。 这很可能是由于这些数据点包含**遗失**或**看不到的值**。\n",
    "- 有1个数据点的 `'RM'` 值为8.78. 这是一个异常值，已经被移除。\n",
    "- 对于本项目，房屋的`'RM'`， `'LSTAT'`，`'PTRATIO'`以及`'MEDV'`特征是必要的，其余不相关特征已经被移除。\n",
    "- `'MEDV'`特征的值已经过必要的数学转换，可以反映35年来市场的通货膨胀效应。\n",
    "\n",
    "运行下面区域的代码以载入波士顿房屋数据集，以及一些此项目所需的Python库。如果成功返回数据集的大小，表示数据集已载入成功。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 载入此项目所需要的库\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 检查你的Python版本\n",
    "from sys import version_info\n",
    "if version_info.major != 2 and version_info.minor != 7:\n",
    "    raise Exception('请使用Python 2.7来完成此项目')\n",
    "    \n",
    "# 让可视化的结果在notebook中显示\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston housing dataset has 489 data points with 4 variables each.\n"
     ]
    }
   ],
   "source": [
    "# 载入波士顿房屋的数据集\n",
    "data = pd.read_csv('housing.csv')\n",
    "prices = data['MEDV']\n",
    "features = data.drop('MEDV', axis = 1)\n",
    "    \n",
    "# 完成\n",
    "print (\"Boston housing dataset has {} data points with {} variables each.\".format(*data.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__下面三张图的横坐标分别是：住宅平均房间数量、区域中被认为是低收入阶层的比率和镇上学生与教师数量比例，纵坐标是房屋的中值价格__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xa2cb908>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20, 10))\n",
    "plt.subplot(2, 2, 1)\n",
    "plt.title('RM')\n",
    "plt.scatter(features.get_values()[:, 0], prices.get_values())\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.title('LSTAT')\n",
    "plt.scatter(features.get_values()[:, 1], prices.get_values())\n",
    "plt.subplot(2, 2, 3)\n",
    "plt.title('PTRATIO')\n",
    "plt.scatter(features.get_values()[:, 2], prices.get_values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第二步. 分析数据\n",
    "在项目的第一个部分，你会对波士顿房地产数据进行初步的观察并给出你的分析。通过对数据的探索来熟悉数据可以让你更好地理解和解释你的结果。\n",
    "\n",
    "由于这个项目的最终目标是建立一个预测房屋价值的模型，我们需要将数据集分为**特征(features)**和**目标变量(target variable)**。\n",
    "- **特征** `'RM'`， `'LSTAT'`，和 `'PTRATIO'`，给我们提供了每个数据点的数量相关的信息。\n",
    "- **目标变量**：` 'MEDV'`，是我们希望预测的变量。\n",
    "\n",
    "他们分别被存在`features`和`prices`两个变量名中。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 1：基础统计运算\n",
    "你的第一个编程练习是计算有关波士顿房价的描述统计数据。我们已为你导入了` numpy `，你需要使用这个库来执行必要的计算。这些统计数据对于分析模型的预测结果非常重要的。\n",
    "在下面的代码中，你要做的是：\n",
    "- 计算`prices`中的`'MEDV'`的最小值、最大值、均值、中值和标准差；\n",
    "- 将运算结果储存在相应的变量中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for Boston housing dataset:\n",
      "\n",
      "Minimum price: $105,000.00\n",
      "Maximum price: $1,024,800.00\n",
      "Mean price: $454,342.94\n",
      "Median price $438,900.00\n",
      "Standard deviation of prices: $165,171.13\n"
     ]
    }
   ],
   "source": [
    "#TODO 1\n",
    "\n",
    "#目标：计算价值的最小值\n",
    "minimum_price = None\n",
    "\n",
    "#目标：计算价值的最大值\n",
    "maximum_price = None\n",
    "\n",
    "#目标：计算价值的平均值\n",
    "mean_price = None\n",
    "\n",
    "#目标：计算价值的中值\n",
    "median_price = None\n",
    "\n",
    "#目标：计算价值的标准差\n",
    "std_price = None\n",
    "\n",
    "maximum_price = np.max(prices)\n",
    "minimum_price = np.min(prices)\n",
    "mean_price = np.mean(prices)\n",
    "median_price = np.median(prices)\n",
    "std_price = np.std(prices)\n",
    "\n",
    "#目标：输出计算的结果\n",
    "print (\"Statistics for Boston housing dataset:\\n\")\n",
    "print (\"Minimum price: ${:,.2f}\".format(minimum_price))\n",
    "print (\"Maximum price: ${:,.2f}\".format(maximum_price))\n",
    "print (\"Mean price: ${:,.2f}\".format(mean_price))\n",
    "print (\"Median price ${:,.2f}\".format(median_price))\n",
    "print (\"Standard deviation of prices: ${:,.2f}\".format(std_price))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 特征观察\n",
    "\n",
    "如前文所述，本项目中我们关注的是其中三个值:`'RM'`、`'LSTAT'` 和`'PTRATIO'`，对每一个数据点:\n",
    "- `'RM'` 是该地区中每个房屋的平均房间数量；\n",
    "- `'LSTAT'` 是指该地区有多少百分比的房东属于是低收入阶层（有工作但收入微薄）；\n",
    "- `'PTRATIO'` 是该地区的中学和小学里，学生和老师的数目比（`学生/老师`）。\n",
    "\n",
    "_凭直觉，上述三个特征中对每一个来说，你认为增大该特征的数值，`'MEDV'`的值会是**增大**还是**减小**呢？每一个答案都需要你给出理由。_\n",
    "\n",
    "**提示：**你预期一个`'RM'` 值是6的房屋跟`'RM'` 值是7的房屋相比，价值更高还是更低呢？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 回答：增大RM，MEDV会增大，房间的品骏数量增大，就会导致房价上涨；增大LSTAT，MEDV会减小，因为低收入家庭虽然收入较少，需要靠租房来获取利润，但是他们经济少，无法花费较大资金来买房，所以房价会减小；增大PTRATIO，MEDV会基本不变化，学生的数量增大，导致学区房价格上涨，但是学区房会高于低收入阶层，不会高于高收入阶层，处于中间状态。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 2: 数据分割与重排\n",
    "接下来，你需要把波士顿房屋数据集分成训练和测试两个子集。通常在这个过程中，数据也会被重排列，以消除数据集中由于顺序而产生的偏差。\n",
    "在下面的代码中，你需要\n",
    "\n",
    "将`features`和`prices`的数据都分成用于训练的数据子集和用于测试的数据子集。\n",
    "  - 分割比例为：80%的数据用于训练，20%用于测试；\n",
    "  - 选定一个数值以设定 `random_seed` ，这会确保结果的一致性；\n",
    "  - 提示：打乱训练集和测试集的数据时，只要创建一个 list，然后用这个 list 分别应用于 X，y 生成训练集和测试集。\n",
    " ```\n",
    " test = np.array([1, 3, 5, 7, 9, 11])\n",
    " \"\"\" test[[0,1,2]] = [1, 3, 5]\n",
    " \"\"\" test[[1,3,5]] = [3, 7, 11]\n",
    " ```\n",
    "  \n",
    "  可能需要用到的函数\n",
    "  - (numpy.random.seed)[https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.seed.html]\n",
    "  - (numpy.random.shuffle)[https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.shuffle.html]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "392\n",
      "97\n",
      "392\n",
      "97\n",
      "(392L, 3L)\n",
      "(392L,)\n"
     ]
    }
   ],
   "source": [
    "LEN, seed = 489, 666\n",
    "\n",
    "def generate_train_and_test(X, y):\n",
    "    np.random.seed(seed)\n",
    "    shuffle_index = np.random.permutation(LEN)#返回一个乱序列\n",
    "    test_size = int(LEN * 0.2)\n",
    "    test_index = shuffle_index[:test_size] #返回测试集的索引序列\n",
    "    train_index = shuffle_index[test_size:] #返回训练集的索引序列\n",
    "    X_test = X[test_index]\n",
    "    y_test = y[test_index]\n",
    "    X_train = X[train_index]\n",
    "    y_train = y[train_index]\n",
    "    return X_train, X_test, y_train, y_test\n",
    "X_train, X_test, y_train, y_test = generate_train_and_test(features.values, prices.values)\n",
    "print(len(X_train))\n",
    "print(len(X_test))\n",
    "print(len(y_train))\n",
    "print(len(y_test))\n",
    "\n",
    "print(X_train.shape)\n",
    "print(y_train.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 训练及测试\n",
    "*将数据集按一定比例分为训练用的数据集和测试用的数据集对学习算法有什么好处？*\n",
    "\n",
    "*如果果用模型已经见过的数据，例如部分训练集数据进行测试，又有什么坏处？*\n",
    "\n",
    "**提示：** 如果没有数据来对模型进行测试，会出现什么问题？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 回答:测试模型的好坏，如果不合适，及时调整参数；如果没有测试集，则可能会出现过拟合或者过拟合现象。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第三步. 模型衡量标准"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习3：定义衡量标准\n",
    "如果不能对模型的训练和测试的表现进行量化地评估，我们就很难衡量模型的好坏。通常我们会定义一些衡量标准，这些标准可以通过对某些误差或者拟合程度的计算来得到。在这个项目中，你将通过运算[*决定系数*](http://stattrek.com/statistics/dictionary.aspx?definition=coefficient_of_determination) R<sup>2</sup> 来量化模型的表现。模型的决定系数是回归分析中十分常用的统计信息，经常被当作衡量模型预测能力好坏的标准。\n",
    "\n",
    "R<sup>2</sup>的数值范围从0至1，表示**目标变量**的预测值和实际值之间的相关程度平方的百分比。一个模型的R<sup>2</sup> 值为0还不如直接用**平均值**来预测效果好；而一个R<sup>2</sup> 值为1的模型则可以对目标变量进行完美的预测。从0至1之间的数值，则表示该模型中目标变量中有百分之多少能够用**特征**来解释。_模型也可能出现负值的R<sup>2</sup>，这种情况下模型所做预测有时会比直接计算目标变量的平均值差很多。_\n",
    "\n",
    "在下方代码的 `performance_metric` 函数中，你要实现：\n",
    "- 计算 `y_true` 和 `y_predict`的R<sup>2</sup>值，作为对其表现的评判，可参考[`r2_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html)。\n",
    "- 将他们的表现评分储存到`score`变量中。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO 3\n",
    "\n",
    "# 提示： 导入r2_score\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "def performance_metric(y_true, y_predict):\n",
    "    \"\"\"计算并返回预测值相比于预测值的分数\"\"\"\n",
    "\n",
    "    score  = r2_score(y_true,y_predict,sample_weight=None,multioutput=None)\n",
    "\n",
    "    return score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 拟合程度\n",
    "\n",
    "假设一个数据集有五个数据且一个模型做出下列目标变量的预测：\n",
    "\n",
    "| 真实数值 | 预测数值 |\n",
    "| :-------------: | :--------: |\n",
    "| 3.0 | 2.5 |\n",
    "| -0.5 | 0.0 |\n",
    "| 2.0 | 2.1 |\n",
    "| 7.0 | 7.8 |\n",
    "| 4.2 | 5.3 |\n",
    "*你觉得这个模型已成功地描述了目标变量的变化吗？如果成功，请解释为什么，如果没有，也请给出原因。*  \n",
    "\n",
    "**提示**：运行下方的代码，使用`performance_metric`函数来计算模型的决定系数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model has a coefficient of determination, R^2, of 0.923.\n"
     ]
    }
   ],
   "source": [
    "# 计算这个模型的预测结果的决定系数\n",
    "score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])\n",
    "print \"Model has a coefficient of determination, R^2, of {:.3f}.\".format(score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 回答:是，模型的预测值和真实值之间的相关程度达到了0.92，可以近似描述了目标变量的变化。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第四步. 模型训练\n",
    "### 编程练习 4：训练回归模型\n",
    "在这个练习中，你将需要将所学到的内容整合，使用 **gradient descent 算法**训练一个线性回归模型。你可以尝试使用自己构建的多项式特征和 L1、L2 Loss，进行实验后，讨论他们是否对你的模型有效，并通过前面定义的 `performance_metric` 量化他们的提升效果。\n",
    "\n",
    "在这里，你不能使用现成 package，不能使用额外 data。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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   ],
   "source": [
    "# TODO 4\n",
    "# 特征放缩　　　\n",
    "def featureScale(X):\n",
    "    resX = np.empty(shape=X.shape, dtype=float)\n",
    "    mean = np.array([np.min(X[:, i]) for i in range(X.shape[1])])\n",
    "    scale = np.array([(np.max(X[:, i] - np.min(X[:, i]))) for i in range(X.shape[1])])\n",
    "    for i in range(X.shape[1]):\n",
    "        #对样本的每一列特征处理\n",
    "        resX[:, i] = (X[:, i] - mean[i]) / scale[i]\n",
    "    return resX\n",
    "\n",
    "# 定义计算目标函数,这里目标函数是均方误差ＭＳＥ\n",
    "def J(X, theta, y):\n",
    "    m = len(y)\n",
    "#     R2 = lamda * np.sum(np.square(theta))\n",
    "    temp = np.sum((X.dot(theta) - y) ** 2) \n",
    "    return temp / (2 * m)\n",
    "\n",
    "# 定义计算求目标函数的梯度　　　　\n",
    "def graJ(X, theta, y):\n",
    "    gra = np.empty(len(theta)) # 先给导数向量开空间，我们要对每个theta求偏导\n",
    "    gra[0] = np.sum(X.dot(theta) - y) #计算第一个特征对应的theta求偏导，因为X1 = 1\n",
    "    for i in range(1, len(theta)):\n",
    "        gra[i] = (X.dot(theta) - y).dot(X[:, i]) #可以看成是两个向量的点乘，第二个向量对应着全部样本的第ｉ列特征\n",
    "    \n",
    "    return gra / len(X)\n",
    "\n",
    "#　梯度下降实现(学习率默认为0.01,默认最多迭代10000次)\n",
    "def gradientDescent(X, theta, y, n_iters=10000, alpha=0.01):\n",
    "    \n",
    "    for i in range(n_iters):\n",
    "        gra = graJ(X, theta, y)\n",
    "        last_theta = theta\n",
    "        theta = theta - alpha * gra \n",
    "        print(J(X, theta, y))\n",
    "    \n",
    "    return theta\n",
    "\n",
    "def train(X, y):\n",
    "    X_train_plus = np.hstack([np.ones((len(X), 1)), X])\n",
    "    init_theta = np.zeros(X_train_plus.shape[1]) #初始化theta向量，长度对应样本中的特征数＋１\n",
    "    theta = gradientDescent(X_train_plus, init_theta, y)#在原来的样本矩阵前加一列特征，特征值都为１,即X1\n",
    "    return theta\n",
    "\n",
    "def predict(X_test, theta):\n",
    "    X_test_plus = np.hstack([np.ones((len(X_test), 1)), X_test])\n",
    "    return X_test_plus.dot(theta)\n",
    "\n",
    "\n",
    "#　测试模型\n",
    "X_train = featureScale(X_train)\n",
    "print(X_train)\n",
    "theta = train(X_train, y_train)\n",
    "print(theta)\n",
    "X_test = featureScale(X_test)\n",
    "y_predict = predict(X_test, theta)\n",
    "print(y_predict.shape)\n",
    "score = performance_metric(y_test, y_predict)\n",
    "print(score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 回归模型的优化\n",
    "在最基础的回归模型上，你使用了什么办法来提升模型的效果，最后模型的性能是否得到了提升？如果提升了，请说出提升性能的原理，如果没有，请探究没有生效的原因。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 回答：使用梯度下降来优化线性函数的参数。选取一个确定的步长，通过对损失函数求导，更新参数的值，使损失函数的值最小，多次迭代，选取最优解。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第六步. 做出预测\n",
    "当我们用数据训练出一个模型，它现在就可用于对新的数据进行预测。在决策树回归函数中，模型已经学会对新输入的数据*提问*，并返回对**目标变量**的预测值。你可以用这个预测来获取数据未知目标变量的信息，这些数据必须是不包含在训练数据之内的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 预测销售价格\n",
    "想像你是一个在波士顿地区的房屋经纪人，并期待使用此模型以帮助你的客户评估他们想出售的房屋。你已经从你的三个客户收集到以下的资讯:\n",
    "\n",
    "| 特征 | 客戶 1 | 客戶 2 | 客戶 3 |\n",
    "| :---: | :---: | :---: | :---: |\n",
    "| 房屋内房间总数 | 5 间房间 | 4 间房间 | 8 间房间 |\n",
    "| 社区贫困指数（％被认为是贫困阶层） | 17% | 32% | 3% |\n",
    "| 邻近学校的学生-老师比例 | 15：1 | 22：1 | 12：1 |\n",
    "\n",
    "*你会建议每位客户的房屋销售的价格为多少？从房屋特征的数值判断，这样的价格合理吗？为什么？* \n",
    "\n",
    "**提示：**用你在**分析数据**部分计算出来的统计信息来帮助你证明你的答案。\n",
    "\n",
    "运行下列的代码区域，使用你的模型来为每位客户的房屋价值做出预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted selling price for Client 1's home: $431,996.54\n",
      "Predicted selling price for Client 2's home: $-109,162.20\n",
      "Predicted selling price for Client 3's home: $868,720.08\n"
     ]
    }
   ],
   "source": [
    "# 生成三个客户的数据\n",
    "client_data = [[5, 17, 15], # 客户 1\n",
    "               [4, 32, 22], # 客户 2\n",
    "               [8, 3, 12]]  # 客户 3\n",
    "\n",
    "# 进行预测\n",
    "client_data = featureScale(np.array(client_data))\n",
    "predicted_price = predict(client_data, theta)\n",
    "for i, price in enumerate(predicted_price):\n",
    "    print \"Predicted selling price for Client {}'s home: ${:,.2f}\".format(i+1, price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 回答：客户1:396000，客户2：200000，客户3：120000。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 5\n",
    "你刚刚预测了三个客户的房子的售价。在这个练习中，你将用你的最优模型在整个测试数据上进行预测, 并计算相对于目标变量的决定系数 R<sup>2</sup>的值**。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal model has R^2 score 0.76 on test data\n"
     ]
    }
   ],
   "source": [
    "#TODO 5\n",
    "\n",
    "# 提示：你可能需要用到 X_test, y_test, performance_metric\n",
    "# 提示：你需要使用编程练习 4 中得到参数数值进行预测\n",
    "# 提示：你可能需要参考问题3的代码来计算R^2的值\n",
    "\n",
    "r2 = 1\n",
    "y_predict = predict(X_test, theta)\n",
    "r2 = performance_metric(y_test, y_predict)\n",
    "print \"Optimal model has R^2 score {:,.2f} on test data\".format(r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题6 - 分析决定系数\n",
    "\n",
    "你刚刚计算了最优模型在测试集上的决定系数，你会如何评价这个结果？（你也可以尝试使用你的模型对问题 5 中三个客户的房屋价值进行预测，并与你之前的预测值进行对比）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题6 - 回答"
   ]
  }
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